This invention generally relates to interferometry and, more particularly, to the use of a selectively rotatable optical sphere in conjunction with mathematical sampling procedures to automatically calibrate an interferometer.
Full aperture interferometers are commonly used to measure the xe2x80x9cfigurexe2x80x9d of optical components. xe2x80x9cFigurexe2x80x9d is typically taken to mean the low spatial frequency departure from nominal. Since interferometers used are comparators, the data reported is, in effect, the difference between two surfaces, a xe2x80x9creferencexe2x80x9d surface and the object under test.
Deducing the departure from nominal of the reference surface itself has been an area of active development for over 100 years. Lord Rayleigh, for example, pioneered the use of liquid surfaces as a xe2x80x9cperfectxe2x80x9d reference for flats. A catalog of well-known methods in optical, as well as mechanical metrology, can be found, inter alia, in Evans C. J, Hocken R. J., and Estler W. T. xe2x80x9cSelf-calibration: reversal, redundancy, error separation and xe2x80x9cabsolute testingxe2x80x9d.xe2x80x9d CIRP Annals, Vol 45/2 (1996) pp617-634.
In optical testing of spherical wavefronts, a number of techniques are known, and all have advantages and disadvantages. One technique known as ball averaging has some significant advantages in conceptual simplicity and ease of implementation. The basic idea of ball averaging to calibrate the spherical wavefront of an interferometer is that the expected value of the average of a number of measurements (made with a perfect instrument) of the surface departure (from a sphere) of sub-aperture segments of a sphere is zero. Since the systematic errors of the instrument appear in every measurement, the expectation value of the average of a number of measurements converges to the systematic error in the instrument.
Parks, Evans, and Shao (Parks R. E., Evans C. J. and Shao L-Z. xe2x80x9cCalibration of interferometer transmission spheresxe2x80x9d OSA xe2x80x98Optical Fabrication and Testing Workshop, Vol 12, 1998 Technical Digest Series, pp80-83) described setting a spherical ball in a kinematic (3-ball) seat, rotating the ball manually between measurements, and then averaging. Evans and Parks (Evans C. J. and Estler W. T. xe2x80x9cSelf-calibration: reversal, redundancy, error separation and xe2x80x9cabsolute testingxe2x80x9d.xe2x80x9d ASPE Tutorial notes (1997 et seq)) also showed that a reasonable ball could be floated in an air bearing seat and data taken as the ball spins. However, due to density variations, the center of mass and the geometric center of the ball will-be different, which causes the ball to tend to settle (eventually) in a fixed orientation. Stopping the ball periodically and restarting rotation with a different set of initial conditions is thus recommended. Epstein (Epstein L. xe2x80x9cA device for deflecting light beams through very small anglesxe2x80x9d Applied Optics, Vol 10(1971) No 1, p73) shows the fabrication of a ball from two optically contacted hemispherical pieces of glass of different refractive index.
Sawyer (Sawyer B. A. (1968) U.S. Pat. No. 3,376,578) described a planar, two-dimensional magnetic positioning device for driving chart plotters and other devices.
The major disadvantages of ball averaging, at least in known implementations, are that:
1. Significant operator intervention and physical handling of the ball, both in set-up and during testing, are required;
2. Coherent reflections between the front and back surfaces of the ball arise if a transmissive ball is used; and
3. The uncertainty of the measurement process decreases at best as the square root of the number of measurements taken.
Consequently, it is a primary purpose of the invention described here to substantially reduce the disadvantages noted above without mitigating any of the advantages.
Another object of the present invention is to provide apparatus and methods by which an optical sphere can be rotatably supported to enable interferometric random sampling of its surface to calibrate an interferometer for subsequent use in measuring test surfaces.
Another object of the present invention is to provide apparatus and methods by which an interferometer may be calibrated by mathematically sampling the average interferometric differences between a wavefront provided by the interferometer and the surface of a rotatable optical sphere.
It is another object of the present invention to provide apparatus and methods by which an interferometer may be automatically calibrated.
Yet another object of the present invention is to provide an optical sphere calibration device that can be used in a variety of orientations.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter when the detailed description is read in conjunction with the drawings.
The present invention is an interferometric apparatus and method for calibrating the spherical wavefront or reference surface of an interferometer by performing appropriate mathematical operations, such as averaging, on the reported results taken at some number of selected positions on the surface of an optical sphere which may be rotating while data is taken or may be stationary while data is taken and rotated between cycles of data acquisition. The apparatus comprises a rotatable, preferably hollow, polished optical sphere constructed from a number (two or greater) of segments with a partially or completely reflecting external surface. Where the external surface is only partially reflecting and the underlying material of construction is transmissive at the operating wavelength of the interferometer, the inner structure of the sphere is made to preclude unwanted reflections of light from other surfaces back to the interferometer. Alternatively, solid spheres may be assembled from segments, for example, if the material of choice does not transmit at the wavelength of the interferometer to be tested or the fabricator prefers such a design.
Also included is a stationary hollow seat or system of xe2x80x9cpointxe2x80x9d constraints which either coarsely or completely define the center of rotation of the sphere. Active or passive devices are preferably imbedded in the sphere and interact, without contact, with complementary devices in the stationary seat and used either to affect ball motions (rotations and/or translations of the ball center) or to sense those motions.
Means are provided, as needed, to levitate and rotate as, for example, air or magnetic bearings. The optical sphere seat may optionally have means to lock ball rotation at some chosen position both during measurement or for protection during shipping and handling.
The means of attaching the optical sphere segments is preferably stable thermally, chemically, and dimensionally. The materials of construction of the optical sphere and seat are preferably of low coefficient of thermal expansion, and the optical sphere is preferably polished or otherwise produced so that the departures from a best fit sphere are small. The exact radius of curvature of the sphere is immaterial to the basic functionality, and is to be selected based on considerations of the specific embodiment of the present invention.